If vertices of a parallelogram are respectively (0, 0) , (1, 0) , (2, 2) and (1, 2) , then angle bet

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9.Straight Line

easy

If vertices of a parallelogram are respectively $(0, 0)$, $(1, 0)$, $(2, 2)$ and $(1, 2)$, then angle between diagonals is

A

$\pi /3$

B

$\pi /2$

C

$3\pi /2$

D

$\pi /4$

Solution

(d)Here,

Slope of Ist diagonal= ${m_1} = \frac{{2 – 0}}{{2 – 0}} = 1$

$\Rightarrow {\theta _1} = {45^o}$

Slope of IInd diagonal= ${m_2} = \frac{{2 – 0}}{{1 – 1}} = \infty $

$\Rightarrow {\theta _2} = {90^o}$

==>${\theta _2} – {\theta _1} = {45^o} = \frac{\pi }{4}$.

Standard 11

Mathematics

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